D) Some powers of the matrix
Matrix^2
30 x 30 sparse Matrix of class "dgCMatrix"
[1,] 4 . 1 2 1 1 2 2 3 . . . . 1 . . 2 2 2 2 1 1 2 1 . 2 2 . . .
[2,] . 6 . 2 . 1 2 1 3 . . 2 . 1 . 1 1 2 3 1 2 . 1 1 1 2 1 1 3 2
[3,] 1 . 7 . . 4 2 . 3 . . 1 1 1 2 1 2 . 2 3 . 4 3 3 . 1 . 2 4 2
[4,] 2 2 . 11 2 . 1 2 2 . 2 3 2 3 2 2 1 3 5 4 5 3 3 1 2 6 5 2 2 .
[5,] 1 . . 2 2 . 1 1 1 . . . . 1 . . . 1 2 1 1 . . . . 1 2 . . .
[6,] 1 1 4 . . 6 2 . 3 . . 3 1 1 2 . 2 1 1 3 1 2 2 3 . 1 . 2 4 2
[7,] 2 2 2 1 1 2 7 1 5 . . . 1 1 1 . 2 2 4 2 3 1 2 2 2 1 1 3 2 2
[8,] 2 1 . 2 1 . 1 4 2 . . . . 2 . . 1 1 2 . . . 2 . 1 4 2 . 1 1
[9,] 3 3 3 2 1 3 5 2 11 . 1 2 2 2 3 2 4 2 5 4 3 2 3 2 2 4 2 3 4 3
[10,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
[11,] . . . 2 . . . . 1 . 3 1 1 . 1 2 . . 1 1 1 . 1 . 1 1 1 1 1 .
[12,] . 2 1 3 . 3 . . 2 . 1 7 2 2 2 2 2 1 1 4 2 2 . 2 1 3 1 2 5 2
[13,] . . 1 2 . 1 1 . 2 . 1 2 5 1 3 2 1 . 1 3 2 1 1 . 1 2 1 1 2 .
[14,] 1 1 1 3 1 1 1 2 2 . . 2 1 6 2 . 1 . 1 2 2 1 1 1 1 3 3 2 1 .
[15,] . . 2 2 . 2 1 . 3 . 1 2 3 2 5 2 1 . . 2 1 1 2 2 . 1 2 2 2 1
[16,] . 1 1 2 . . . . 2 . 2 2 2 . 2 5 1 . 1 2 1 1 2 . . 1 1 1 2 2
[17,] 2 1 2 1 . 2 2 1 4 . . 2 1 1 1 1 5 . 2 2 1 2 2 2 1 2 1 2 3 2
[18,] 2 2 . 3 1 1 2 1 2 . . 1 . . . . . 5 3 2 3 . 2 . . 2 2 . . 1
[19,] 2 3 2 5 2 1 4 2 5 . 1 1 1 1 . 1 2 3 10 3 3 3 3 1 4 4 3 2 2 2
[20,] 2 1 3 4 1 3 2 . 4 . 1 4 3 2 2 2 2 2 3 9 4 3 . 2 1 3 1 . 3 1
[21,] 1 2 . 5 1 1 3 . 3 . 1 2 2 2 1 1 1 3 3 4 8 2 2 . 2 2 2 1 1 1
[22,] 1 . 4 3 . 2 1 . 2 . . 2 1 1 1 1 2 . 3 3 2 8 2 4 1 3 1 2 3 1
[23,] 2 1 3 3 . 2 2 2 3 . 1 . 1 1 2 2 2 2 3 . 2 2 8 1 1 2 2 3 2 2
[24,] 1 1 3 1 . 3 2 . 2 . . 2 . 1 2 . 2 . 1 2 . 4 1 6 . 1 1 2 3 1
[25,] . 1 . 2 . . 2 1 2 . 1 1 1 1 . . 1 . 4 1 2 1 1 . 5 2 . 3 2 1
[26,] 2 2 1 6 1 1 1 4 4 . 1 3 2 3 1 1 2 2 4 3 2 3 2 1 2 10 3 . 5 1
[27,] 2 1 . 5 2 . 1 2 2 . 1 1 1 3 2 1 1 2 3 1 2 1 2 1 . 3 6 1 . .
[28,] . 1 2 2 . 2 3 . 3 . 1 2 1 2 2 1 2 . 2 . 1 2 3 2 3 . 1 8 3 2
[29,] . 3 4 2 . 4 2 1 4 . 1 5 2 1 2 2 3 . 2 3 1 3 2 3 2 5 . 3 10 3
[30,] . 2 2 . . 2 2 1 3 . . 2 . . 1 2 2 1 2 1 1 1 2 1 1 1 . 2 3 5
Matrix^5
30 x 30 sparse Matrix of class "dgCMatrix"
[1,] 290 372 550 710 126 514 469 264 820 . 163 588 343 388 388
[2,] 372 498 585 902 184 619 635 279 1041 . 214 728 448 464 475
[3,] 550 585 488 1404 340 472 707 562 1188 . 287 699 487 699 492
[4,] 710 902 1404 1406 270 1330 1358 561 2170 . 373 1263 803 857 1006
[5,] 126 184 340 270 40 313 254 103 435 . 76 304 177 169 215
[6,] 514 619 472 1330 313 476 711 506 1164 . 277 690 460 611 454
[7,] 469 635 707 1358 254 711 710 440 1309 . 351 1000 642 668 650
[8,] 264 279 562 561 103 506 440 166 729 . 129 500 310 320 367
[9,] 820 1041 1188 2170 435 1164 1309 729 2212 . 516 1510 996 1080 997
[10,] . . . . . . . . . . . . . . .
[11,] 163 214 287 373 76 277 351 129 516 . 104 283 214 218 242
[12,] 588 728 699 1263 304 690 1000 500 1510 . 283 744 520 616 555
[13,] 343 448 487 803 177 460 642 310 996 . 214 520 366 412 393
[14,] 388 464 699 857 169 611 668 320 1080 . 218 616 412 430 480
[15,] 388 475 492 1006 215 454 650 367 997 . 242 555 393 480 418
[16,] 299 389 408 738 163 408 578 262 843 . 175 470 331 415 358
[17,] 487 558 595 1230 264 573 717 435 1204 . 274 745 511 603 520
[18,] 265 444 597 648 105 615 523 224 892 . 165 680 363 385 434
[19,] 685 867 1233 1627 312 1215 1150 579 2020 . 415 1387 904 950 1004
[20,] 675 919 936 1503 338 916 1180 658 1890 . 352 1045 665 789 707
[21,] 470 738 890 1113 201 889 921 423 1556 . 310 1011 607 629 701
[22,] 638 649 721 1344 318 687 883 604 1490 . 291 791 550 743 621
[23,] 493 585 770 1339 262 745 772 429 1307 . 315 932 602 741 703
[24,] 486 491 450 1136 265 434 612 473 1021 . 234 568 396 538 410
[25,] 323 389 535 777 153 520 546 247 968 . 223 616 462 423 495
[26,] 778 847 1279 1501 335 1195 1307 573 2070 . 342 1161 755 839 874
[27,] 373 474 847 809 133 775 710 293 1149 . 213 739 454 478 568
[28,] 466 534 572 1322 267 551 688 414 1183 . 346 766 596 633 629
[29,] 842 905 874 1914 474 867 1253 699 1958 . 411 1054 756 925 772
[30,] 380 479 423 1050 229 446 569 333 938 . 230 638 430 524 426
[1,] 299 487 265 685 675 470 638 493 486 323 778 373 466 842
[2,] 389 558 444 867 919 738 649 585 491 389 847 474 534 905
[3,] 408 595 597 1233 936 890 721 770 450 535 1279 847 572 874
[4,] 738 1230 648 1627 1503 1113 1344 1339 1136 777 1501 809 1322 1914
[5,] 163 264 105 312 338 201 318 262 265 153 335 133 267 474
[6,] 408 573 615 1215 916 889 687 745 434 520 1195 775 551 867
[7,] 578 717 523 1150 1180 921 883 772 612 546 1307 710 688 1253
[8,] 262 435 224 579 658 423 604 429 473 247 573 293 414 699
[9,] 843 1204 892 2020 1890 1556 1490 1307 1021 968 2070 1149 1183 1958
[10,] . . . . . . . . . . . . . .
[11,] 175 274 165 415 352 310 291 315 234 223 342 213 346 411
[12,] 470 745 680 1387 1045 1011 791 932 568 616 1161 739 766 1054
[13,] 331 511 363 904 665 607 550 602 396 462 755 454 596 756
[14,] 415 603 385 950 789 629 743 741 538 423 839 478 633 925
[15,] 358 520 434 1004 707 701 621 703 410 495 874 568 629 772
[16,] 264 434 330 759 603 594 481 516 352 403 647 419 539 636
[17,] 434 628 527 1122 987 872 788 736 520 507 1144 684 604 964
[18,] 330 527 276 665 723 489 609 495 528 325 722 331 533 943
[19,] 759 1122 665 1554 1672 1198 1301 1140 1018 733 1700 892 1088 1867
[20,] 603 987 723 1672 1296 1114 1040 1096 773 803 1577 849 986 1543
[21,] 594 872 489 1198 1114 856 908 897 739 603 1177 603 921 1430
[22,] 481 788 609 1301 1040 908 840 951 608 564 1339 841 737 1106
[23,] 516 736 495 1140 1096 897 951 846 715 536 1200 773 826 1171
[24,] 352 520 528 1018 773 739 608 715 386 424 1055 677 479 751
[25,] 403 507 325 733 803 603 564 536 424 336 744 434 491 793
[26,] 647 1144 722 1700 1577 1177 1339 1200 1055 744 1534 858 1098 1686
[27,] 419 684 331 892 849 603 841 773 677 434 858 434 763 1127
[28,] 539 604 533 1088 986 921 737 826 479 491 1098 763 662 925
[29,] 636 964 943 1867 1543 1430 1106 1171 751 793 1686 1127 925 1340
[30,] 355 473 458 894 846 773 585 552 387 405 904 580 468 739
[1,] 380
[2,] 479
[3,] 423
[4,] 1050
[5,] 229
[6,] 446
[7,] 569
[8,] 333
[9,] 938
[10,] .
[11,] 230
[12,] 638
[13,] 430
[14,] 524
[15,] 426
[16,] 355
[17,] 473
[18,] 458
[19,] 894
[20,] 846
[21,] 773
[22,] 585
[23,] 552
[24,] 387
[25,] 405
[26,] 904
[27,] 580
[28,] 468
[29,] 739
[30,] 360
Matrix^15
30 x 30 sparse Matrix of class "dgCMatrix"
[1,] 166916953792 203858972671 245355934813 3.941182e+11 83200580582
[2,] 203858972671 248920359158 299308575155 4.814376e+11 101676857449
[3,] 245355934813 299308575155 358766619198 5.799037e+11 122637078371
[4,] 394118192366 481437640008 579903661460 9.301291e+11 196319313374
[5,] 83200580582 101676857449 122637078371 1.963193e+11 41408384258
[6,] 237626708664 289903185532 347551708677 5.615869e+11 118756326376
[7,] 272580086016 332781084505 399872085829 6.439685e+11 136024822459
[8,] 144996605861 177120958113 213393606881 3.422525e+11 72225521422
[9,] 448242201021 547205674652 657479254152 1.058838e+12 223685115884
[10,] . . . . .
[11,] 93843662859 114604098238 137894146526 2.215333e+11 46779774250
[12,] 275604118471 336378930714 403923580257 6.508991e+11 137569380813
[13,] 182189436655 222418219491 267273668242 4.302227e+11 90896885456
[14,] 207142925805 252950940612 304339735182 4.890247e+11 103265557058
[15,] 199074725026 242961652090 291685734541 4.702544e+11 99390198024
[16,] 160134988211 195478316535 234841338459 3.781902e+11 79910330218
[17,] 240966572011 294091507375 353084233537 5.692965e+11 120311214403
[18,] 174278187579 212926717778 256536061195 4.113734e+11 86804208683
[19,] 389413724141 475581744621 572285619704 9.195028e+11 194127710531
[20,] 348048809891 424914366271 510633463191 8.218963e+11 173640753356
[21,] 287575655661 351261535196 422821564799 6.788819e+11 143314879025
[22,] 280354120977 342158085236 410845862057 6.622228e+11 139955396698
[23,] 272671965872 332893553427 400148853081 6.440670e+11 136037586450
[24,] 206534678237 251972518927 302145993239 4.880610e+11 103202198697
[25,] 179729103346 219468896017 263969573649 4.244366e+11 89626697884
[26,] 380995008557 465259230327 559864476300 8.993978e+11 189915470975
[27,] 222082081514 271315208463 326944758586 5.241110e+11 110597448810
[28,] 243746599288 297463277262 357033800184 5.759637e+11 121727534240
[29,] 375025543975 457617073319 549092787230 8.860169e+11 187308412418
[30,] 193873427543 236585938581 283876201474 4.581465e+11 96840100221
[1,] 237626708664 272580086016 144996605861 4.482422e+11 . 93843662859
[2,] 289903185532 332781084505 177120958113 5.472057e+11 . 114604098238
[3,] 347551708677 399872085829 213393606881 6.574793e+11 . 137894146526
[4,] 561586926684 643968514444 342252548575 1.058838e+12 . 221533270097
[5,] 118756326376 136024822459 72225521422 2.236851e+11 . 46779774250
[6,] 336684562552 387329219536 206655862240 6.368430e+11 . 133547792769
[7,] 387329219536 444771119842 236897817751 7.314149e+11 . 153264201524
[8,] 206655862240 236897817751 125906056550 3.895600e+11 . 81518352617
[9,] 636843008064 731414937715 389559984272 1.202702e+12 . 251988036238
[10,] . . . . . .
[11,] 133547792769 153264201524 81518352617 2.519880e+11 . 52746741008
[12,] 391241248581 449659450506 239549035021 7.392575e+11 . 154867533017
[13,] 258869581143 297360412490 158326028870 4.888882e+11 . 102390266873
[14,] 294746025033 338257479049 179945881053 5.561666e+11 . 116428003314
[15,] 282530933856 324744570719 173052924490 5.339184e+11 . 111881693990
[16,] 227463294108 261324491317 139168891967 4.296464e+11 . 89999499780
[17,] 342014586071 393041316348 209467257321 6.462711e+11 . 135446283003
[18,] 248442317180 284773512035 151339191510 4.682959e+11 . 97990537681
[19,] 554271466823 635889553088 338279135876 1.045670e+12 . 218937659809
[20,] 494582710670 568060159399 302463615426 9.339812e+11 . 195606756819
[21,] 409496397517 469734769072 249788526572 7.723880e+11 . 161666268768
[22,] 397950318132 457332851701 243699332239 7.519416e+11 . 157557028615
[23,] 387575545744 444997102745 236948537147 7.317489e+11 . 153298486137
[24,] 292689890804 336675553336 179606005020 5.535570e+11 . 116068465047
[25,] 255669169065 293423778657 156145380770 4.825012e+11 . 101046888638
[26,] 542216656747 622190569718 330946386418 1.023015e+12 . 214135532668
[27,] 316609888497 362924696914 192836407791 5.967643e+11 . 124846961500
[28,] 345849259314 397512896686 211902550386 6.536395e+11 . 137027043652
[29,] 531889301145 611571349575 326041820241 1.005507e+12 . 210755095629
[30,] 274993663855 316132544864 168557314820 5.198217e+11 . 108983692204
[1,] 275604118471 182189436655 207142925805 199074725026 160134988211
[2,] 336378930714 222418219491 252950940612 242961652090 195478316535
[3,] 403923580257 267273668242 304339735182 291685734541 234841338459
[4,] 650899074066 430222698040 489024748625 470254394384 378190211083
[5,] 137569380813 90896885456 103265557058 99390198024 79910330218
[6,] 391241248581 258869581143 294746025033 282530933856 227463294108
[7,] 449659450506 297360412490 338257479049 324744570719 261324491317
[8,] 239549035021 158326028870 179945881053 173052924490 139168891967
[9,] 739257468435 488888171497 556166610294 533918379181 429646354142
[10,] . . . . .
[11,] 154867533017 102390266873 116428003314 111881693990 89999499780
[12,] 454148404510 300390967860 341832010099 328034299351 263995025056
[13,] 300390967860 198655989978 226000127589 216985382614 174598418761
[14,] 341832010099 226000127589 256996814000 246939248506 198647225583
[15,] 328034299351 216985382614 246939248506 236932688858 190690157327
[16,] 263995025056 174598418761 198647225583 190690157327 153447553452
[17,] 397158369102 262700599785 298945671007 286833439232 230853162032
[18,] 287980621700 190323124244 216298814865 208031578482 167301442055
[19,] 642906002596 425023768081 483249679988 464389303978 373567280526
[20,] 573920910188 379529730580 431759782057 414547066884 333566100946
[21,] 474827506586 313880847936 356843446981 343006454827 275903004459
[22,] 462018615036 305597449235 347770177774 333704456434 268561532527
[23,] 449825301321 297459408371 338353530249 324901386768 261421026219
[24,] 340071045760 225004555864 256177123917 245590894895 197711184600
[25,] 296624078033 196125076940 223024951688 214258146160 172373801566
[26,] 628783531941 415700121009 472688392559 454231125746 365383500782
[27,] 366912979379 242492765170 275593420690 265084312950 213169319484
[28,] 401698870029 265729966877 302412906433 290113395000 233509495818
[29,] 617747600224 408673164547 465168467307 446153107938 359118152207
[30,] 319451977772 211329439027 240526134520 230694777935 185696866968
[1,] 240966572011 174278187579 3.894137e+11 348048809891 287575655661
[2,] 294091507375 212926717778 4.755817e+11 424914366271 351261535196
[3,] 353084233537 256536061195 5.722856e+11 510633463191 422821564799
[4,] 569296481048 411373379042 9.195028e+11 821896295115 678881904020
[5,] 120311214403 86804208683 1.941277e+11 173640753356 143314879025
[6,] 342014586071 248442317180 5.542715e+11 494582710670 409496397517
[7,] 393041316348 284773512035 6.358896e+11 568060159399 469734769072
[8,] 209467257321 151339191510 3.382791e+11 302463615426 249788526572
[9,] 646271088053 468295907950 1.045670e+12 933981221969 772387971233
[10,] . . . . .
[11,] 135446283003 97990537681 2.189377e+11 195606756819 161666268768
[12,] 397158369102 287980621700 6.429060e+11 573920910188 474827506586
[13,] 262700599785 190323124244 4.250238e+11 379529730580 313880847936
[14,] 298945671007 216298814865 4.832497e+11 431759782057 356843446981
[15,] 286833439232 208031578482 4.643893e+11 414547066884 343006454827
[16,] 230853162032 167301442055 3.735673e+11 333566100946 275903004459
[17,] 347203150648 251811123732 5.620995e+11 501882356711 415225223335
[18,] 251811123732 181901041336 4.066195e+11 363579137201 300243093604
[19,] 562099524358 406619491272 9.084866e+11 811945314527 670937339117
[20,] 501882356711 363579137201 8.119453e+11 725094705568 599626605917
[21,] 415225223335 300243093604 6.709373e+11 599626605917 495429341430
[22,] 403979536975 292944250003 6.539639e+11 583845498699 483027328748
[23,] 393246412863 284827465814 6.360956e+11 568251269958 469842596190
[24,] 297300650853 215914232236 4.817403e+11 429881187353 355892312677
[25,] 259334172050 187704203581 4.192915e+11 374667441051 309681703974
[26,] 549899048335 397814425221 8.888216e+11 794190741027 656325400919
[27,] 320895622296 231773133965 5.181435e+11 463245678866 382548273814
[28,] 351138220253 254746348421 5.685815e+11 507643667586 420055664753
[29,] 540105942419 391977114558 8.747796e+11 780797246052 646207380847
[30,] 279230506468 202645856629 4.522382e+11 403736889749 334118132542
[1,] 280354120977 272671965872 206534678237 179729103346 3.809950e+11
[2,] 342158085236 332893553427 251972518927 219468896017 4.652592e+11
[3,] 410845862057 400148853081 302145993239 263969573649 5.598645e+11
[4,] 662222772603 644067049572 488060951391 424436631873 8.993978e+11
[5,] 139955396698 136037586450 103202198697 89626697884 1.899155e+11
[6,] 397950318132 387575545744 292689890804 255669169065 5.422167e+11
[7,] 457332851701 444997102745 336675553336 293423778657 6.221906e+11
[8,] 243699332239 236948537147 179606005020 156145380770 3.309464e+11
[9,] 751941638982 731748861542 553556952226 482501195979 1.023015e+12
[10,] . . . . .
[11,] 157557028615 153298486137 116068465047 101046888638 2.141355e+11
[12,] 462018615036 449825301321 340071045760 296624078033 6.287835e+11
[13,] 305597449235 297459408371 225004555864 196125076940 4.157001e+11
[14,] 347770177774 338353530249 256177123917 223024951688 4.726884e+11
[15,] 333704456434 324901386768 245590894895 214258146160 4.542311e+11
[16,] 268561532527 261421026219 197711184600 172373801566 3.653835e+11
[17,] 403979536975 393246412863 297300650853 259334172050 5.498990e+11
[18,] 292944250003 284827465814 215914232236 187704203581 3.978144e+11
[19,] 653963881152 636095643276 481740329529 419291458504 8.888216e+11
[20,] 583845498699 568251269958 429881187353 374667441051 7.941907e+11
[21,] 483027328748 469842596190 355892312677 309681703974 6.563254e+11
[22,] 469997156952 457554777947 345918598705 301719092797 6.397059e+11
[23,] 457554777947 445210075236 336889783589 293527434178 6.223347e+11
[24,] 345918598705 336889783589 254443546764 222215337528 4.712581e+11
[25,] 301719092797 293527434178 222215337528 193500752206 4.102020e+11
[26,] 639705925249 622334705515 471258080311 410202021190 8.693991e+11
[27,] 373293366817 362986073297 275157904865 239186316676 5.068520e+11
[28,] 408575017400 397753488116 300639732859 262317398103 5.562633e+11
[29,] 628392633527 611878174633 462356688247 403553709289 8.556767e+11
[30,] 324910035022 316316074285 239048403494 208631633335 4.424450e+11
[1,] 222082081514 243746599288 3.750255e+11 193873427543
[2,] 271315208463 297463277262 4.576171e+11 236585938581
[3,] 326944758586 357033800184 5.490928e+11 283876201474
[4,] 524110964936 575963724235 8.860169e+11 458146461898
[5,] 110597448810 121727534240 1.873084e+11 96840100221
[6,] 316609888497 345849259314 5.318893e+11 274993663855
[7,] 362924696914 397512896686 6.115713e+11 316132544864
[8,] 192836407791 211902550386 3.260418e+11 168557314820
[9,] 596764300611 653639474724 1.005507e+12 519821650924
[10,] . . . .
[11,] 124846961500 137027043652 2.107551e+11 108983692204
[12,] 366912979379 401698870029 6.177476e+11 319451977772
[13,] 242492765170 265729966877 4.086732e+11 211329439027
[14,] 275593420690 302412906433 4.651685e+11 240526134520
[15,] 265084312950 290113395000 4.461531e+11 230694777935
[16,] 213169319484 233509495818 3.591182e+11 185696866968
[17,] 320895622296 351138220253 5.401059e+11 279230506468
[18,] 231773133965 254746348421 3.919771e+11 202645856629
[19,] 518143528384 568581536674 8.747796e+11 452238233828
[20,] 463245678866 507643667586 7.807972e+11 403736889749
[21,] 382548273814 420055664753 6.462074e+11 334118132542
[22,] 373293366817 408575017400 6.283926e+11 324910035022
[23,] 362986073297 397753488116 6.118782e+11 316316074285
[24,] 275157904865 300639732859 4.623567e+11 239048403494
[25,] 239186316676 262317398103 4.035537e+11 208631633335
[26,] 506852025940 556263342482 8.556767e+11 442444959090
[27,] 295305833876 324662131244 4.994776e+11 258253795410
[28,] 324662131244 355120324590 5.462126e+11 282376413345
[29,] 499477575967 546212615423 8.400304e+11 434341158788
[30,] 258253795410 282376413345 4.343412e+11 224538320698
Matrix^30
30 x 30 sparse Matrix of class "dgCMatrix"
[1,] 1.974669e+24 2.410792e+24 2.897662e+24 4.663533e+24 9.851244e+23
[2,] 2.410792e+24 2.943238e+24 3.537640e+24 5.693515e+24 1.202698e+24
[3,] 2.897662e+24 3.537640e+24 4.252093e+24 6.843342e+24 1.445586e+24
[4,] 4.663533e+24 5.693515e+24 6.843342e+24 1.101377e+25 2.326548e+24
[5,] 9.851244e+23 1.202698e+24 1.445586e+24 2.326548e+24 4.914601e+23
[6,] 2.806589e+24 3.426452e+24 4.118449e+24 6.628255e+24 1.400151e+24
[7,] 3.222866e+24 3.934667e+24 4.729295e+24 7.611371e+24 1.607825e+24
[8,] 1.715938e+24 2.094919e+24 2.517995e+24 4.052495e+24 8.560491e+23
[9,] 5.299256e+24 6.469646e+24 7.776228e+24 1.251513e+25 2.643695e+24
[10,] . . . . .
[11,] 1.109963e+24 1.355108e+24 1.628778e+24 2.621375e+24 5.537390e+23
[12,] 3.256955e+24 3.976285e+24 4.779320e+24 7.691878e+24 1.624831e+24
[13,] 2.153761e+24 2.629439e+24 3.160469e+24 5.086489e+24 1.074469e+24
[14,] 2.449937e+24 2.991027e+24 3.595079e+24 5.785962e+24 1.222226e+24
[15,] 2.352500e+24 2.872073e+24 3.452106e+24 5.555847e+24 1.173616e+24
[16,] 1.892878e+24 2.310938e+24 2.777645e+24 4.470367e+24 9.443196e+23
[17,] 2.847751e+24 3.476704e+24 4.178847e+24 6.725469e+24 1.420687e+24
[18,] 2.062705e+24 2.518272e+24 3.026846e+24 4.871448e+24 1.029045e+24
[19,] 4.606563e+24 5.623965e+24 6.759750e+24 1.087922e+25 2.298126e+24
[20,] 4.114639e+24 5.023396e+24 6.037898e+24 9.717452e+24 2.052713e+24
[21,] 3.402265e+24 4.153686e+24 4.992540e+24 8.035055e+24 1.697325e+24
[22,] 3.313119e+24 4.044853e+24 4.861736e+24 7.824518e+24 1.652850e+24
[23,] 3.224121e+24 3.936198e+24 4.731134e+24 7.614334e+24 1.608451e+24
[24,] 2.439470e+24 2.978251e+24 3.579730e+24 5.761239e+24 1.217003e+24
[25,] 2.125688e+24 2.595166e+24 3.119272e+24 5.020191e+24 1.060465e+24
[26,] 4.506319e+24 5.501580e+24 6.612649e+24 1.064248e+25 2.248116e+24
[27,] 2.628384e+24 3.208886e+24 3.856931e+24 6.207399e+24 1.311251e+24
[28,] 2.880405e+24 3.516570e+24 4.226764e+24 6.802586e+24 1.436977e+24
[29,] 4.430688e+24 5.409248e+24 6.501683e+24 1.046385e+25 2.210382e+24
[30,] 2.290779e+24 2.796720e+24 3.361536e+24 5.410080e+24 1.142824e+24
[1,] 2.806589e+24 3.222866e+24 1.715938e+24 5.299256e+24 . 1.109963e+24
[2,] 3.426452e+24 3.934667e+24 2.094919e+24 6.469646e+24 . 1.355108e+24
[3,] 4.118449e+24 4.729295e+24 2.517995e+24 7.776228e+24 . 1.628778e+24
[4,] 6.628255e+24 7.611371e+24 4.052495e+24 1.251513e+25 . 2.621375e+24
[5,] 1.400151e+24 1.607825e+24 8.560491e+23 2.643695e+24 . 5.537390e+23
[6,] 3.989006e+24 4.580653e+24 2.438854e+24 7.531820e+24 . 1.577586e+24
[7,] 4.580653e+24 5.260058e+24 2.800590e+24 8.648945e+24 . 1.811575e+24
[8,] 2.438854e+24 2.800590e+24 1.491108e+24 4.604921e+24 . 9.645301e+23
[9,] 7.531820e+24 8.648945e+24 4.604921e+24 1.422118e+25 . 2.978715e+24
[10,] . . . . . .
[11,] 1.577586e+24 1.811575e+24 9.645301e+23 2.978715e+24 . 6.239107e+23
[12,] 4.629105e+24 5.315696e+24 2.830212e+24 8.740428e+24 . 1.830737e+24
[13,] 3.061135e+24 3.515165e+24 1.871564e+24 5.779873e+24 . 1.210630e+24
[14,] 3.482086e+24 3.998553e+24 2.128934e+24 6.574693e+24 . 1.377111e+24
[15,] 3.343606e+24 3.839530e+24 2.044264e+24 6.313216e+24 . 1.322342e+24
[16,] 2.690343e+24 3.089376e+24 1.644863e+24 5.079762e+24 . 1.063988e+24
[17,] 4.047505e+24 4.647832e+24 2.474624e+24 7.642280e+24 . 1.600723e+24
[18,] 2.931712e+24 3.366550e+24 1.792441e+24 5.535510e+24 . 1.159448e+24
[19,] 6.547291e+24 7.518394e+24 4.002990e+24 1.236225e+25 . 2.589352e+24
[20,] 5.848126e+24 6.715525e+24 3.575519e+24 1.104212e+25 . 2.312841e+24
[21,] 4.835624e+24 5.552852e+24 2.956484e+24 9.130376e+24 . 1.912415e+24
[22,] 4.708931e+24 5.407361e+24 2.879017e+24 8.891151e+24 . 1.862307e+24
[23,] 4.582434e+24 5.262105e+24 2.801681e+24 8.652310e+24 . 1.812280e+24
[24,] 3.467218e+24 3.981475e+24 2.119837e+24 6.546611e+24 . 1.371228e+24
[25,] 3.021233e+24 3.469346e+24 1.847170e+24 5.704534e+24 . 1.194851e+24
[26,] 6.404813e+24 7.354784e+24 3.915880e+24 1.209324e+25 . 2.533005e+24
[27,] 3.735708e+24 4.289796e+24 2.284001e+24 7.053574e+24 . 1.477416e+24
[28,] 4.093916e+24 4.701126e+24 2.502999e+24 7.729911e+24 . 1.619077e+24
[29,] 6.297334e+24 7.231353e+24 3.850156e+24 1.189028e+25 . 2.490493e+24
[30,] 3.255883e+24 3.738795e+24 1.990629e+24 6.147580e+24 . 1.287648e+24
[1,] 3.256955e+24 2.153761e+24 2.449937e+24 2.352500e+24 1.892878e+24
[2,] 3.976285e+24 2.629439e+24 2.991027e+24 2.872073e+24 2.310938e+24
[3,] 4.779320e+24 3.160469e+24 3.595079e+24 3.452106e+24 2.777645e+24
[4,] 7.691878e+24 5.086489e+24 5.785962e+24 5.555847e+24 4.470367e+24
[5,] 1.624831e+24 1.074469e+24 1.222226e+24 1.173616e+24 9.443196e+23
[6,] 4.629105e+24 3.061135e+24 3.482086e+24 3.343606e+24 2.690343e+24
[7,] 5.315696e+24 3.515165e+24 3.998553e+24 3.839530e+24 3.089376e+24
[8,] 2.830212e+24 1.871564e+24 2.128934e+24 2.044264e+24 1.644863e+24
[9,] 8.740428e+24 5.779873e+24 6.574693e+24 6.313216e+24 5.079762e+24
[10,] . . . . .
[11,] 1.830737e+24 1.210630e+24 1.377111e+24 1.322342e+24 1.063988e+24
[12,] 5.371923e+24 3.552346e+24 4.040847e+24 3.880143e+24 3.122054e+24
[13,] 3.552346e+24 2.349097e+24 2.672133e+24 2.565862e+24 2.064553e+24
[14,] 4.040847e+24 2.672133e+24 3.039593e+24 2.918706e+24 2.348460e+24
[15,] 3.880143e+24 2.565862e+24 2.918706e+24 2.802629e+24 2.255061e+24
[16,] 3.122054e+24 2.064553e+24 2.348460e+24 2.255061e+24 1.814476e+24
[17,] 4.696994e+24 3.106029e+24 3.533155e+24 3.392642e+24 2.729799e+24
[18,] 3.402158e+24 2.249781e+24 2.559162e+24 2.457381e+24 1.977267e+24
[19,] 7.597918e+24 5.024355e+24 5.715281e+24 5.487980e+24 4.415759e+24
[20,] 6.786558e+24 4.487817e+24 5.104960e+24 4.901934e+24 3.944212e+24
[21,] 5.611585e+24 3.710832e+24 4.221129e+24 4.053251e+24 3.261342e+24
[22,] 5.464558e+24 3.613604e+24 4.110529e+24 3.947053e+24 3.175892e+24
[23,] 5.317764e+24 3.516533e+24 4.000110e+24 3.841024e+24 3.090578e+24
[24,] 4.023589e+24 2.660720e+24 3.026607e+24 2.906241e+24 2.338429e+24
[25,] 3.506042e+24 2.318477e+24 2.637303e+24 2.532416e+24 2.037642e+24
[26,] 7.432578e+24 4.915018e+24 5.590910e+24 5.368555e+24 4.319666e+24
[27,] 4.335170e+24 2.866764e+24 3.260989e+24 3.131295e+24 2.519515e+24
[28,] 4.750852e+24 3.141645e+24 3.573667e+24 3.431544e+24 2.761100e+24
[29,] 7.307844e+24 4.832532e+24 5.497077e+24 5.278460e+24 4.247172e+24
[30,] 3.778342e+24 2.498543e+24 2.842129e+24 2.729099e+24 2.195897e+24
[1,] 2.847751e+24 2.062705e+24 4.606563e+24 4.114639e+24 3.402265e+24
[2,] 3.476704e+24 2.518272e+24 5.623965e+24 5.023396e+24 4.153686e+24
[3,] 4.178847e+24 3.026846e+24 6.759750e+24 6.037898e+24 4.992540e+24
[4,] 6.725469e+24 4.871448e+24 1.087922e+25 9.717452e+24 8.035055e+24
[5,] 1.420687e+24 1.029045e+24 2.298126e+24 2.052713e+24 1.697325e+24
[6,] 4.047505e+24 2.931712e+24 6.547291e+24 5.848126e+24 4.835624e+24
[7,] 4.647832e+24 3.366550e+24 7.518394e+24 6.715525e+24 5.552852e+24
[8,] 2.474624e+24 1.792441e+24 4.002990e+24 3.575519e+24 2.956484e+24
[9,] 7.642280e+24 5.535510e+24 1.236225e+25 1.104212e+25 9.130376e+24
[10,] . . . . .
[11,] 1.600723e+24 1.159448e+24 2.589352e+24 2.312841e+24 1.912415e+24
[12,] 4.696994e+24 3.402158e+24 7.597918e+24 6.786558e+24 5.611585e+24
[13,] 3.106029e+24 2.249781e+24 5.024355e+24 4.487817e+24 3.710832e+24
[14,] 3.533155e+24 2.559162e+24 5.715281e+24 5.104960e+24 4.221129e+24
[15,] 3.392642e+24 2.457381e+24 5.487980e+24 4.901934e+24 4.053251e+24
[16,] 2.729799e+24 1.977267e+24 4.415759e+24 3.944212e+24 3.261342e+24
[17,] 4.106864e+24 2.974711e+24 6.643315e+24 5.933894e+24 4.906545e+24
[18,] 2.974711e+24 2.154668e+24 4.811937e+24 4.298081e+24 3.553948e+24
[19,] 6.643315e+24 4.811937e+24 1.074632e+25 9.598747e+24 7.936899e+24
[20,] 5.933894e+24 4.298081e+24 9.598747e+24 8.573722e+24 7.089336e+24
[21,] 4.906545e+24 3.553948e+24 7.936899e+24 7.089336e+24 5.861948e+24
[22,] 4.777991e+24 3.460826e+24 7.728938e+24 6.903587e+24 5.708353e+24
[23,] 4.649640e+24 3.367861e+24 7.521320e+24 6.718138e+24 5.555013e+24
[24,] 3.518066e+24 2.548226e+24 5.690864e+24 5.083155e+24 4.203095e+24
[25,] 3.065543e+24 2.220457e+24 4.958865e+24 4.429320e+24 3.662464e+24
[26,] 6.498748e+24 4.707224e+24 1.051247e+25 9.389866e+24 7.764183e+24
[27,] 3.790498e+24 2.745566e+24 6.131568e+24 5.476791e+24 4.528587e+24
[28,] 4.153955e+24 3.008820e+24 6.719490e+24 6.001935e+24 4.962806e+24
[29,] 6.389686e+24 4.628218e+24 1.033603e+25 9.232281e+24 7.633873e+24
[30,] 3.303631e+24 2.392907e+24 5.343994e+24 4.773325e+24 3.946907e+24
[1,] 3.313119e+24 3.224121e+24 2.439470e+24 2.125688e+24 4.506319e+24
[2,] 4.044853e+24 3.936198e+24 2.978251e+24 2.595166e+24 5.501580e+24
[3,] 4.861736e+24 4.731134e+24 3.579730e+24 3.119272e+24 6.612649e+24
[4,] 7.824518e+24 7.614334e+24 5.761239e+24 5.020191e+24 1.064248e+25
[5,] 1.652850e+24 1.608451e+24 1.217003e+24 1.060465e+24 2.248116e+24
[6,] 4.708931e+24 4.582434e+24 3.467218e+24 3.021233e+24 6.404813e+24
[7,] 5.407361e+24 5.262105e+24 3.981475e+24 3.469346e+24 7.354784e+24
[8,] 2.879017e+24 2.801681e+24 2.119837e+24 1.847170e+24 3.915880e+24
[9,] 8.891151e+24 8.652310e+24 6.546611e+24 5.704534e+24 1.209324e+25
[10,] . . . . .
[11,] 1.862307e+24 1.812280e+24 1.371228e+24 1.194851e+24 2.533005e+24
[12,] 5.464558e+24 5.317764e+24 4.023589e+24 3.506042e+24 7.432578e+24
[13,] 3.613604e+24 3.516533e+24 2.660720e+24 2.318477e+24 4.915018e+24
[14,] 4.110529e+24 4.000110e+24 3.026607e+24 2.637303e+24 5.590910e+24
[15,] 3.947053e+24 3.841024e+24 2.906241e+24 2.532416e+24 5.368555e+24
[16,] 3.175892e+24 3.090578e+24 2.338429e+24 2.037642e+24 4.319666e+24
[17,] 4.777991e+24 4.649640e+24 3.518066e+24 3.065543e+24 6.498748e+24
[18,] 3.460826e+24 3.367861e+24 2.548226e+24 2.220457e+24 4.707224e+24
[19,] 7.728938e+24 7.521320e+24 5.690864e+24 4.958865e+24 1.051247e+25
[20,] 6.903587e+24 6.718138e+24 5.083155e+24 4.429320e+24 9.389866e+24
[21,] 5.708353e+24 5.555013e+24 4.203095e+24 3.662464e+24 7.764183e+24
[22,] 5.558790e+24 5.409465e+24 4.092974e+24 3.566502e+24 7.560747e+24
[23,] 5.409465e+24 5.264152e+24 3.983023e+24 3.470696e+24 7.357647e+24
[24,] 4.092974e+24 3.983023e+24 3.013684e+24 2.626037e+24 5.567024e+24
[25,] 3.566502e+24 3.470696e+24 2.626037e+24 2.288257e+24 4.850954e+24
[26,] 7.560747e+24 7.357647e+24 5.567024e+24 4.850954e+24 1.028370e+25
[27,] 4.409926e+24 4.291466e+24 3.247054e+24 2.829398e+24 5.998138e+24
[28,] 4.832778e+24 4.702955e+24 3.558406e+24 3.100694e+24 6.573265e+24
[29,] 7.433863e+24 7.234167e+24 5.473603e+24 4.769541e+24 1.011111e+25
[30,] 3.843497e+24 3.740249e+24 2.829993e+24 2.465975e+24 5.227702e+24
[1,] 2.628384e+24 2.880405e+24 4.430688e+24 2.290779e+24
[2,] 3.208886e+24 3.516570e+24 5.409248e+24 2.796720e+24
[3,] 3.856931e+24 4.226764e+24 6.501683e+24 3.361536e+24
[4,] 6.207399e+24 6.802586e+24 1.046385e+25 5.410080e+24
[5,] 1.311251e+24 1.436977e+24 2.210382e+24 1.142824e+24
[6,] 3.735708e+24 4.093916e+24 6.297334e+24 3.255883e+24
[7,] 4.289796e+24 4.701126e+24 7.231353e+24 3.738795e+24
[8,] 2.284001e+24 2.502999e+24 3.850156e+24 1.990629e+24
[9,] 7.053574e+24 7.729911e+24 1.189028e+25 6.147580e+24
[10,] . . . .
[11,] 1.477416e+24 1.619077e+24 2.490493e+24 1.287648e+24
[12,] 4.335170e+24 4.750852e+24 7.307844e+24 3.778342e+24
[13,] 2.866764e+24 3.141645e+24 4.832532e+24 2.498543e+24
[14,] 3.260989e+24 3.573667e+24 5.497077e+24 2.842129e+24
[15,] 3.131295e+24 3.431544e+24 5.278460e+24 2.729099e+24
[16,] 2.519515e+24 2.761100e+24 4.247172e+24 2.195897e+24
[17,] 3.790498e+24 4.153955e+24 6.389686e+24 3.303631e+24
[18,] 2.745566e+24 3.008820e+24 4.628218e+24 2.392907e+24
[19,] 6.131568e+24 6.719490e+24 1.033603e+25 5.343994e+24
[20,] 5.476791e+24 6.001935e+24 9.232281e+24 4.773325e+24
[21,] 4.528587e+24 4.962806e+24 7.633873e+24 3.946907e+24
[22,] 4.409926e+24 4.832778e+24 7.433863e+24 3.843497e+24
[23,] 4.291466e+24 4.702955e+24 7.234167e+24 3.740249e+24
[24,] 3.247054e+24 3.558406e+24 5.473603e+24 2.829993e+24
[25,] 2.829398e+24 3.100694e+24 4.769541e+24 2.465975e+24
[26,] 5.998138e+24 6.573265e+24 1.011111e+25 5.227702e+24
[27,] 3.498513e+24 3.833961e+24 5.897465e+24 3.049140e+24
[28,] 3.833961e+24 4.201587e+24 6.462955e+24 3.341513e+24
[29,] 5.897465e+24 6.462955e+24 9.941429e+24 5.139973e+24
[30,] 3.049140e+24 3.341513e+24 5.139973e+24 2.657498e+24
